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On effective PDEs of quantum physics. (English) Zbl 1428.35419

D’Abbicco, Marcello (ed.) et al., New tools for nonlinear PDEs and application. Proceedings of the 11th ISAAC congress, Växjö, Sweden, August 14–18, 2017. Cham: Birkhäuser. Trends Math., 1-47 (2019).
Summary: The Hartree-Fock equation is a key effective equation of quantum physics. We review the standard derivation of this equation and its properties and present some recent results on its natural extensions – the density functional, Bogolubov-de Gennes and Hartree-Fock-Bogolubov equations. This paper is based on a talk given at ISAAC2017.
For the entire collection see [Zbl 1417.35003].

MSC:

35Q40 PDEs in connection with quantum mechanics
78A35 Motion of charged particles
35B10 Periodic solutions to PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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